1
$\begingroup$

How could I calculate the total 𝛥𝑣 required to change the inclination of a Geostationary orbit to another circular orbit with an inclination of 30° and the same radius? (The sidereal day is used for Geostationary orbit calculation.)

Currently my idea is to solve it from the formula of inclination, $$\arccos\left(\frac{hk}{|h|}\right)$$ where $h = rv$ and the change from zero to 30 degrees means the component of $h$ on the $k$ axis is increasing.

Since $r$ does not change and $hk$ is changing, the velocity $v$ should change. I'm not too sure what to do next.

$\endgroup$
4
  • $\begingroup$ My idea now is to solve it from the formula of inclination, arccos(hk/|h|). where h = r*v. And the change from 0 degrees to 30 degrees means the component of h on the k axis is increasing. Since r does not change, and hk is changing, the velocity v should change. I'm not too sure what to do next. $\endgroup$ Nov 13, 2019 at 16:47
  • 1
    $\begingroup$ en.m.wikipedia.org/wiki/Orbital_inclination_change $\endgroup$ Nov 13, 2019 at 17:23
  • $\begingroup$ Did you just want the equation, or were you also interested in how the equation is derived? $\endgroup$
    – uhoh
    Nov 13, 2019 at 17:56
  • $\begingroup$ I just want the equation, thanks $\endgroup$ Nov 14, 2019 at 7:14

1 Answer 1

1
$\begingroup$

According to Wikipedia, the general equation for inclination change is:

$$\Delta{v_i}= {2\sin(\frac{\Delta{i}}{2})\sqrt{1-e^2}\cos(\omega+f)na \over {(1+e\cos(f))}}$$

Where:

  • $e\,$ is the orbital eccentricity
  • $\omega\,$ is the argument of periapsis
  • $f\,$ is the true anomaly
  • $n\,$ is the mean motion
  • $a\,$ is the semi-major axis

For circular orbits, this simplifies considerably to:

$$\Delta{v_i}= {2v\, \sin \left(\frac{\Delta{i}}{2} \right)}$$

Where $v\,$ is the orbital velocity and has the same units as $\Delta{v_i}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.